Transcript Warm up f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9 1.

Warm up
f(x) = 3x + 5, g(x) = x – 15, h(x) = 5x, k(x) = -9
1. Find 2f(x) + g(x).
2. Find h(x) k(x).
3. Find g(x) – f(x) – k(x).
CCGPS Alg
2/20/2013
UNIT QUESTION: How do we graph
functions, and what can be done to
change the way they look?
Today’s Question:
How do we write the function to
represent a sequence?
CCGPS Alg
2/20/2013
(I.N. p71)
MCC9-12.F.BF.2 Write arithmetic
and geometric sequences both
recursively and with an explicit
formula, use them to model
situations, and translate between the
two forms.
Arithmetic & Geometric
Sequences
Recursive
Recursive Formula
a formula used to find
the next term of a
sequence when the
previous term is known
Recursive Formula for
Arithmetic Sequence
an  an1  d
Ex:
The first term is 1 for an = an-1 – 2.
Find the next two terms.
a2  an1  2
a2  1 2
a2  1
a3  an1  2
a3  1 2
a3  3
Recursive Formula for
Geometric Sequence
an  an1  r 
Ex:
The first term is 320 for an = -1/4 an-1.
Find the next two terms.
 1
 1
a2     an1 a3     an1
 4
 4
 1
 1
a3     80 
a2    320
4
4
a2  80
a3  20
Find the next term and write the rule
and the recursive formula.
x
1
2
3
4
n
y
3
13
23
33
next term: 43
d  10
an  an1  d
a1  3, an  an1  10
Find the next term and write the rule
and the recursive formula.
x
1
2
3
4
n
y
16
40
100
250
next term: 625
40
r
 2.5
16
an  an1  r 
a1  16, an  2.5an1
Find the next term and write the rule
and the recursive formula.
x
1
2
3
4
n
y
2
14
98
686
next term: 4802
14
r
7
2
an  an1  r 
a1  2, an  7an1
Find the next term and write the rule
and the recursive formula.
x
1
2
3
4
n
y
19
13
7
1
next term: -5
d  6
an  an1  d
a1  19, an  an1  6
Write the rule, the explicit formula
and the recursive formula.
a1 = 15 and d = 5
Explicit : an  a1   n  1 d Recursive : an  an1  d
an  15   n  1 5
an  15  5n  5
an  5n  10
a1  15, an  an1  5
Write the rule, the explicit formula
and the recursive formula.
a1 = 4 and r = 0.2
Explicit : an  a1  r 
an  4  0.2 
n1
n1
Recursive : an  an1  r 
a1  4, an  0.2an1